Many cranes used in construction, shipping, and manufacture suspend the load by ropes ("falls") from a suspension point usually, but not always, the end of a boom or jib, that can be rotated ("slewed") and raised or lowered ("luffed"), providing motion of the suspension point in three-dimensional space. The height of the load is controlled by boom or jib luffing and/or by shortening or lengthening the falls ("hoisting"). Luffing and slewing cause the suspension point to move perpendicular to the line of the boom. It may or may not be possible to move that point in and out along that line (through, for example, telescoping the boom). Some crane configurations provide control in two or three degrees of freedom for some point on the falls other than the boom tip, using restraints such as taglines that run to the falls from near the base of the crane. Such mechanisms effectively move the suspension point to the point in the falls that is so controlled.
Regardless of the mechanism, if the suspension point is accelerated in more than one horizontal direction, the resulting pendulum motion ("sway") of the load is three-dimensional. When the suspension point is no longer being accelerated and the sway is within the "linear regime", the horizontal orbit of the load is elliptical. When the sway is large enough to be noticeably nonlinear, the orbit is similar to an ellipse that precesses in the direction of revolution.
Sway is a major problem in transporting loads quickly and safely, and results in huge costs to the construction, cargo-loading, and heavy manufacturing industries. In current practice, sway is minimized by keeping the suspension-point acceleration levels low, by the use of direct manual control of the load using tag lines, and by operator action in "catching" the load at the end of each move. All of these mechanisms slow the load-handling operation considerably, and additionally endanger the personnel involved.
The extent of motion of the suspension point is constrained by the physical dimensions and capabilities of the crane. For example, the crane may only be capable of luffing and slewing a single boom, wherein the suspension point is constrained to the surface of sphere. All boom-type cranes have a minimum distance from the boom base ("jib radius"), from which the load can be suspended. Other motion constraints are imposed by the load weight. For example, the load may have a maximum jib radius and a maximum lateral sway angle for a given load, due to stability and strength limitations of the crane structure.
The primary sources of sway are the actions of the crane itself and motion of the crane base. Additional, lesser causes are hoisting while swaying, non-vertical pick-up of the load, and forces on the load due to external agents such as wind and manual tagline manipulation.
The problem of controlling sway during operation of cranes of level-beam design, wherein the load is transported from a suspension mechanism moving horizontal along a single axis by moving a trolley out along a beam, has been studied extensively, and several automatic systems to solve that problem have been developed. In such level-beam cranes, sway induced by suspension-point accelerations and by hoisting is effectively planar, and can be efficiently and smoothly removed by a previously disclosed "double pulse" anti-sway control law whereby the sway induced by an initial acceleration is removed by a second acceleration of the same sign, magnitude, and duration, timed to commence one-half a sway period after commencement of the first pulse. To meet a given velocity reference, the first acceleration pulse is of sufficient length to accelerate to one-half the reference velocity; the second acceleration pulse then accelerates the trolley to the full reference velocity. To stop the load, the reference velocity is simply set to zero, and the same double-pulse method is applied to decelerate to this new reference without residual sway. The double-pulse approach for two-dimensional cranes is taught by U.S. Pat. Nos. 4,756,432, 3,517,830, 5,127,533 and 5,526,946.
In the three-dimensional case of the present invention, the anti-sway problem is complicated by the fact that the desired accelerations and velocities are vectors rather than scalars, and that these vectors may not be attainable within the constraints. Furthermore, the sway in two arbitrary horizontal directions is a coupled motion.
Accordingly, while a number of anti-sway approaches apply to cranes wherein the motion of the load suspension point is constrained to a straight, horizontal line, no such law has been previously applied successfully to rotating-boom or other three-degree-of-freedom systems, where the pendulum swings in three dimensions rather than two.